2020/05/28 by Hyuntae Cho, Cho, Hyuntae, Yesom Park +3 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Advection #Applied mathematics #Classical mechanics #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #Convection #Convection–diffusion equation #Convergence (economics) #Diffusion #FOS: Mathematics #FOS: Physical sciences #Finite difference method #Interface (matter) #Interpolation (computer graphics) #Jump #Lattice Boltzmann Simulation Studies #Mathematical analysis #Mathematics #Mechanics #Motion (physics) #Numerical Analysis (math.NA) #Physics #Thermodynamics #Truncation (statistics) #Truncation error #cs.NA #math.NA #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.2005.13717
published in arXiv (Cornell University) (Cornell University)
arxiv created 2020/05/28 · openalex publication_date 2020/05/28 · arxiv updated 2020/05/29 · openalex created_date 2020/06/05 · openalex updated_date 2026/07/28
In this paper, we present a second-order accurate finite-difference method for solving convectiondiffusion equations with interfacial jumps on a moving interface. The proposed method is constructed under a semi-Lagrangian framework for convection-diffusion equations; a novel interpolation scheme is developed in the presence of jump conditions. Combined with a second-order ghost fluid method [3], a sharp capturing method with a first-order local truncation error near the interface and second-order truncation error away from the interface is developed for the convectiondiffusion equation. In addition, a level-set advection algorithm is presented when the velocity gradient jumps across the interface. Numerical experiments support the conclusion that the proposed methods for convection-diffusion equations and level-set advection are necessary for the second-order convergence solution and the interface position.